A Computational Search for Cubic-Like Bent Functions

Boolean functions are a central topic in computer science. A subset of Boolean functions, Bent Boolean functions, provide optimal resistance to various cryptographical attack vectors, making them an interesting subject for cryptography, as well as many other branches of mathematics and computer science. In this work, we search for cubic Bent Boolean functions using a novel characterization presented by Carlet & Villa in [CV23]. We implement a tool for the search of Bent Boolean functions and cubic-like Bent Boolean functions, allowing for constraints to be set on the form of the ANF of Boolean functions generated by the tool; reducing the search space required for an exhaustive search. The tool guarantees efficient traversal of the search space without redundancies. We use this tool to perform an exhaustive search for cubic-like Bent Boolean functions in dimension 6. This search proves unfeasible for dimension 8 and higher. We further attempt to find novel instances of Bent functions that are not Maioarana-McFarland in dimension 10 but fail to find any interesting results. We conclude that the proposed characterization does not yield a significant enough reduction of the search space to make the classification of cubic Bent Boolean functions of dimensions 8 or higher viable; nor could we use it to produce new instances of cubic Bent Boolean functions in 10 variables.Masteroppgave i informatikkINF399MAMN-PROGMAMN-IN

Metrical properties of the set of bent functions in view of duality

In the paper, we give a review of metrical properties of the entire set of bent functions and its significant subclasses of self-dual and anti-self-dual bent functions. We present results for iterative construction of bent functions in n + 2 variables based on the concatenation of four bent functions and consider related open problem proposed by one of the authors. Criterion of self-duality of such functions is discussed. It is explored that the pair of sets of bent functions and affine functions as well as a pair of sets of self-dual and anti-self-dual bent functions in n > 4 variables is a pair of mutually maximally distant sets that implies metrical duality. Groups of automorphisms of the sets of bent functions and (anti-)self-dual bent functions are discussed. The solution to the problem of preserving bentness and the Hamming distance between bent function and its dual within automorphisms of the set of all Boolean functions in n variables is considered